THE░GRaPHIe_theoRy + sTory

Theographie is the investigation and visual examination that explores the relationships between theory, intellectualism, concept, narrative, media and style.

In an age of oversaturation, there is an overwhelming push to simplify. Simplicity of message, ease of use, intuitive solutions and clear directives. As attention spans have shortened, so too has an attempt to embrace and confront cognitive complexity. Spoonfed simplicity begets the same, sometimes out of necessity, but also out of fear of unqualified intellect. Existing on the periphery of traditional corporate communications, Theographie aims to enhance and broaden the manner in which visual designers think, problem solve, research, explore and experiment.

Theorgraphs are an exploration-based, mind-centric approach to visual communication that embraces the fusion of theory with the conveyance of knowledge through layered meaning and story telling.

Attributes of theographie /// 01 complexity in favor of simplicity 02 interpretive in favor of self-evident 03 layered in favor of a singularity 03 research in favor of anecdotal 04 unconventional in favor of traditional

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Immanuel Kant, Critique of Pure Reason [1881]
Of Space
By means of our external sense, a property of our mind, we represent to ourselves objects as external or outside ourselves, and all of these in space. It is within space that their form, size, and relative position are fixed or can be fixed. The internal sense by means of which the mind perceives itself or its internal state, does not give an intuition of the soul itself, as an object, but it is nevertheless a fixed form under which alone an intuition of its internal state is possible, so that whatever belongs to its internal determinations must be represented in relations of time. Time cannot be perceived externally, as little as space can be perceived as something within us.
What then are space and time? Are they real beings? Or, if not that, are they determinations or relations of things, but such as would belong to them even if they were not perceived? Or lastly, are they determinations and relations which are inherent in the form of intuition only, and therefore in the subjective nature of our mind, without which such predicates as space and time would never be ascribed to anything?
In order to understand this more clearly, let us first consider space.
1. Space is not an empirical concept which has been derived from external experience. For in order that certain sensations should be referred to something outside myself, i.e. to something in a different part of space from that where I am; again, in order that I may be able to represent them as side by side, that is, not only as different, but as in different places, the representation of space must already be there. Therefore the representation of space cannot be borrowed through experience from relations of external phenomena, but, on the contrary, this external experience becomes possible only by means of the representation of space.
2. Space is a necessary representation a priori, forming the very foundation of all external intuitions. It is impossible to imagine that there should be no space, though one might very well imagine that there should be space without objects to fill it. Space is therefore regarded as a condition of the possibility of phenomena, not as a determination produced by them; it is a representation a priori which necessarily precedes all external phenomena.
[3. On this necessity of an a priori representation of space rests the apodictic certainty of all geometrical principles, and the possibility of their construction a priori. For if the intuition of space were a concept gained a posteriori, borrowed from general external experience, the first principles of mathematical definition would be nothing but perceptions. They would be exposed to all the accidents of perception, and there being but one straight line between two points would not be a necessity, but only something taught in each case by experience. Whatever is derived from experience possesses a relative generality only, based on induction. We should therefore not be able to say more than that, so far as hitherto observed, no space has yet been found having more than three dimensions.]
4. Space is not a discursive or so-called general concept of the relations of things in general, but a pure intuition. For, first of all, we can imagine one space only and if we speak of many spaces, we mean parts only of one and the same space. Nor can these parts be considered as antecedent to the one and all-embracing space and, as it were, its component parts out of which an aggregate is formed, but they can be thought of as existing within it only. Space is essentially one; its multiplicity, and therefore the general concept of spaces in general, arises entirely from limitations. Hence it follows that, with respect to space, an intuition a priori, which is not empirical, must form the foundation of all conceptions of space. In the same manner all geometrical principles, e.g. ‘that in every triangle two sides together are greater than the third,’ are never to be derived from the general concepts of side and triangle, but from an intuition, and that a priori, with apodictic certainty.
5. Space is represented as an infinite quantity. Now a general concept of space, which is found in a foot as well as in an ell, could tell us nothing in respect to the quantity of the space. If there were not infinity in the progression of intuition, no concept of relations of space could ever contain a principle of infinity.
Of Time
I. Time is not an empirical concept deduced from any experience, for neither coexistence nor succession would enter into our perception, if the representation of time were not given a priori. Only when this representation a priori is given, can we imagine that certain things happen at the same time (simultaneously) or at different times (successively).
II. Time is a necessary representation on which all intuitions depend. We cannot take away time from phenomena in general, though we can well take away phenomena out of time. Time therefore is given a priori. In time alone is reality of phenomena possible. All phenomena may vanish, but time itself (as the general condition of their possibility) cannot be done away with.
III. On this a priori necessity depends also the possibility of apodictic principles of the relations of time, or of axioms of time in general. Time has one dimension only; different times are not simultaneous, but successive, while different spaces are never successive, but simultaneous. Such principles cannot be derived from experience, because experience could not impart to them absolute universality nor apodictic certainty. We should only be able to say that common experience teaches us that it is so, but not that it must be so. These principles are valid as rules under which alone experience is possible; they teach us before experience, not by means of experience.1
IV. Time is not a discursive, or what is called a general concept, but a pure form of sensuous intuition. Different times are parts only of one and the same time. Representation, which can be produced by a single object only, is called an intuition. The proposition that different times cannot exist at the same time cannot be deduced from any general concept. Such a proposition is synthetical, and cannot be deduced from concepts only. It is contained immediately in the intuition and representation of time.
V. To say that time is infinite means no more than that every definite quantity of time is possible only by limitations of one time which forms the foundation of all times. The original representation of time must therefore be given as unlimited. But when the parts themselves and every quantity of an object can be represented as determined by limitation only, the whole representation cannot be given by concepts (for in that case the partial representations come first), but it must be founded on immediate intuition.
Of Ideas in General
In spite of the great wealth of our languages, a thoughtful mind is often at a loss for an expression that should square exactly with its concept; and for want of which he cannot make himself altogether intelligible, either to others or to himself. To coin new words is to arrogate to oneself legislative power in matters of language, a proceeding which seldom succeeds, so that, before taking so desperate a step, it is always advisable to look about, in dead and learned languages, whether they do not contain such a concept and its adequate expression. Even if it should happen that the original meaning of the word had become somewhat uncertain, through carelessness on the part of its authors, it is better nevertheless to determine and fix the meaning which principally belonged to it (even if it should remain doubtful whether it was originally used exactly in that meaning), than to spoil our labour by becoming unintelligible.
Whenever therefore there exists one single word only for a certain concept, which, in its received meaning, exactly covers that concept, and when it is of great consequence to keep that concept distinct from other related concepts, we ought not to be lavish in using it nor employ it, for the sake of variety only, as a synonyme in the place of others, but carefully preserve its own peculiar meaning, as otherwise it may easily happen that the expression ceases to attract special attention, and loses itself in a crowd of other words of very different import, so that the thought, which that expression alone could have preserved, is lost with it.
From the way in which Plato uses the term idea, it is easy to see that he meant by it something which not only was never borrowed from the senses, but which even far transcends the concepts of the understanding, with which Aristotle occupied himself, there being nothing in experience corresponding to the ideas. With him the ideas are archetypes of things themselves, not only, like the categories, keys to possible experiences. According to his opinion they flowed out from the highest reason, which however exists no longer in its original state, but has to recall, with difficulty, the old but now very obscure ideas, which it does by means of reminiscence, commonly called philosophy. I shall not enter here on any literary discussions in order to determine the exact meaning which the sublime philosopher himself connected with that expression. I shall only remark, that it is by no means unusual, in ordinary conversations, as well as in written works, that by carefully comparing the thoughts uttered by an author on his own subject, we succeed in understanding him better than he understood himself, because he did not sufficiently define his concept, and thus not only spoke, but sometimes even thought, in opposition to his own intentions.
Plato knew very well that our faculty of knowledge was filled with a much higher craving than merely to spell out phenomena according to a synthetical unity, and thus to read and understand them as experience. He knew that our reason, if left to itself, tries to soar up to knowledge to which no object that experience may give can ever correspond; but which nevertheless is real, and by no means a mere cobweb of the brain.
Plato discovered his ideas principally in what is practical,1 that is, in what depends on freedom, which again belongs to a class of knowledge which is a peculiar product of reason. He who would derive the concept of virtue from experience, and would change what at best could only serve as an example or an imperfect illustration, into a type and a source of knowledge (as many have really done), would indeed transform virtue into an equivocal phantom, changing according to times and circumstances, and utterly useless to serve as a rule. Everybody can surely perceive that, when a person is held up to us as a model of virtue, we have always in our own mind the true original with which we compare this so-called model, and estimate it accordingly. The true original is the idea of virtue, in regard to which all possible objects of experience may serve as examples (proofs of the practicability, in a certain degree, of that which is required by the concept of reason), but never as archetypes. That no man can ever act up to the pure idea of virtue does not in the least prove the chimerical nature of that concept; for every judgment as to the moral worth or unworth of actions is possible by means of that idea only, which forms, therefore, the necessary foundation for every approach to moral perfection, however far the impediments inherent in human nature, the extent of which it is difficult to determine, may keep us removed from it.
The Platonic Republic has been supposed to be a striking example of purely imaginary perfection. It has become a byword, as something that could exist in the brain of an idle thinker only, and Brucker thinks it ridiculous that Plato could have said that no prince could ever govern well, unless he participated in the ideas. We should do better, however, to follow up this thought and endeavour (where that excellent philosopher leaves us without his guidance) to place it in a clearer light by our own efforts, rather than to throw it aside as useless, under the miserable and very dangerous pretext of its impracticability. A constitution founded on the greatest possible human freedom, according to laws which enable the freedom of each individual to exist by the side of the freedom of others (without any regard to the highest possible human happiness, because that must necessarily follow by itself), is, to say the least, a necessary idea, on which not only the first plan of a constitution or a state, but all laws must be based, it being by no means necessary to take account from the beginning of existing impediments, which may owe their origin not so much to human nature itself as to the actual neglect of true ideas in legislation. For nothing can be more mischievous and more unworthy a philosopher than the vulgar appeal to what is called adverse experience, which possibly might never have existed, if at the proper time institutions had been framed according to those ideas, and not according to crude concepts, which, because they were derived from experience only, have marred all good intentions. The more legislation and government are in harmony with that idea, the rarer, no doubt, punishments would become; and it is therefore quite rational to say (as Plato did), that in a perfect state no punishments would be necessary. And though this can never be realised, yet the idea is quite correct which sets up this maximum as an archetype, in order thus to bring our legislative constitutions nearer and nearer to the greatest possible perfection. Which may be the highest degree where human nature must stop, and how wide the chasm may be between the idea and its realisation, no one can or ought to determine, because it is this very freedom that may be able to transcend any limits hitherto assigned to it.
It is not only, however, where human reason asserts its free causality and ideas become operative agents (with regard to actions and their objects), that is to say, in the sphere of ethics, but also in nature itself, that Plato rightly discovered clear proofs of its origin from ideas. A plant, an animal, the regular plan of the cosmos (most likely therefore the whole order of nature), show clearly that they are possible according to ideas only; and that though no single creature, under the singular conditions of its existence, can fully correspond with the idea of what is most perfect of its kind (as little as any individual man with the idea of humanity, which, for all that, he carries in his mind as the archetype of all his actions), those ideas are nevertheless determined throughout in the highest understanding each by itself as unchangeable, and are in fact the original causes of things, although it can only be said of the whole of them, connected together in the universe, that it is perfectly adequate to the idea. If we make allowance for the exaggerated expression, the effort of the philosopher to ascend from the mere observing and copying of the physical side of nature to an architectonic system of it, teleologically, that is according to ideas, deserves respect and imitation, while with regard to the principles of morality, legislation, and religion, where it is the ideas themselves that make experience of the good possible, though they can never be fully realised in experience, such efforts are of very eminent merit, which those only fail to recognise who attempt to judge it according to empirical rules, the very validity of which, as principles, was meant to be denied by Plato. With regard to nature, it is experience no doubt which supplies us with rules, and is the foundation of all truth: with regard to moral laws, on the contrary, experience is, alas! but the source of illusion; and it is altogether reprehensible to derive or limit the laws of what we ought to do according to our experience of what has been done.
Instead of considering these subjects, the full development of which constitutes in reality the peculiar character and dignity of philosophy, we have to occupy ourselves at present with a task less brilliant, though not less useful, of building and strengthening the foundation of that majestic edifice of morality, which at present is undermined by all sorts of mole-tracks, the work of our reason, which thus vainly, but always with the same confidence, is searching for buried treasures. It is our duty at present to acquire an accurate knowledge of the transcendental use of the pure reason, its principles and ideas, in order to be able to determine and estimate correctly their influence and value. But before I leave this preliminary introduction, I beg those who really care for philosophy (which means more than is commonly supposed), if they are convinced by what I have said and shall still have to say, to take the term idea, in its original meaning, under their special protection, so that it should no longer be lost among other expressions, by which all sorts of representations are loosely designated, to the great detriment of philosophy. There is no lack of names adequate to express every kind of representation, without our having to encroach on the property of others. I shall give a graduated list of them. The whole class may be called representation (repraesentatio). Under it stands conscious representation, perception (perceptio). A perception referring to the subject only, as a modification of his state, is sensation (sensatio), while an objective sensation is called knowledge, cognition (cognitio). Cognition is either intuition or concept (intuitus vel conceptus). The former refers immediately to an object and is singular, the latter refers to it mediately, that is, by means of a characteristic mark that can be shared by several things in common. A concept is either empirical or pure, and the pure concept, so far as it has its origin in the understanding only (not in the pure image of sensibility) is called notion (notio). A concept formed of notions and transcending all possible experience is an idea, or a concept of reason. To any one who has once accustomed himself to these distinctions, it must be extremely irksome to hear the representation of red colour called an idea, though it could not even be rightly called a notion (a concept of the understanding).
Of Trowing, Knowing, and Believing
The holding a thing to be true is an event in our understanding which, though it may rest on objective grounds, requires also subjective causes in the mind of the person who is to judge. If the judgment is valid for everybody, if only he is possessed of reason, then the ground of it is objectively sufficient, and the holding it to be true is called conviction. If, on the contrary, it has its ground in the peculiar character of the subject only, it is called persuasion.
Persuasion is a mere illusion, the ground of the judgment, though it lies solely in the subject, being regarded as objective. Such a judgment has, therefore, private validity only, and the holding it to be true cannot be communicated to others. Truth, however, depends on agreement with the object, and, with regard to it, the judgments of every understanding must agree with each other. An external criterion, therefore, as to whether our holding a thing to be true be conviction or only persuasion, consists in the possibility of communicating it, and finding its truth to be valid for the reason of every man. For, in that case, there is at least a presumption that the ground of the agreement of all judgments, in spite of the diversity of the subjects, rests upon the common ground, namely, on the object with which they all agree, and thus prove the truth of the judgment.

Immanuel Kant, Critique of Pure Reason [1881]
Of Space
By means of our external sense, a property of our mind, we represent to ourselves objects as external or outside ourselves, and all of these in space. It is within space that their form, size, and relative position are fixed or can be fixed. The internal sense by means of which the mind perceives itself or its internal state, does not give an intuition of the soul itself, as an object, but it is nevertheless a fixed form under which alone an intuition of its internal state is possible, so that whatever belongs to its internal determinations must be represented in relations of time. Time cannot be perceived externally, as little as space can be perceived as something within us.
What then are space and time? Are they real beings? Or, if not that, are they determinations or relations of things, but such as would belong to them even if they were not perceived? Or lastly, are they determinations and relations which are inherent in the form of intuition only, and therefore in the subjective nature of our mind, without which such predicates as space and time would never be ascribed to anything?
In order to understand this more clearly, let us first consider space.
1. Space is not an empirical concept which has been derived from external experience. For in order that certain sensations should be referred to something outside myself, i.e. to something in a different part of space from that where I am; again, in order that I may be able to represent them as side by side, that is, not only as different, but as in different places, the representation of space must already be there. Therefore the representation of space cannot be borrowed through experience from relations of external phenomena, but, on the contrary, this external experience becomes possible only by means of the representation of space.
2. Space is a necessary representation a priori, forming the very foundation of all external intuitions. It is impossible to imagine that there should be no space, though one might very well imagine that there should be space without objects to fill it. Space is therefore regarded as a condition of the possibility of phenomena, not as a determination produced by them; it is a representation a priori which necessarily precedes all external phenomena.
[3. On this necessity of an a priori representation of space rests the apodictic certainty of all geometrical principles, and the possibility of their construction a priori. For if the intuition of space were a concept gained a posteriori, borrowed from general external experience, the first principles of mathematical definition would be nothing but perceptions. They would be exposed to all the accidents of perception, and there being but one straight line between two points would not be a necessity, but only something taught in each case by experience. Whatever is derived from experience possesses a relative generality only, based on induction. We should therefore not be able to say more than that, so far as hitherto observed, no space has yet been found having more than three dimensions.]
4. Space is not a discursive or so-called general concept of the relations of things in general, but a pure intuition. For, first of all, we can imagine one space only and if we speak of many spaces, we mean parts only of one and the same space. Nor can these parts be considered as antecedent to the one and all-embracing space and, as it were, its component parts out of which an aggregate is formed, but they can be thought of as existing within it only. Space is essentially one; its multiplicity, and therefore the general concept of spaces in general, arises entirely from limitations. Hence it follows that, with respect to space, an intuition a priori, which is not empirical, must form the foundation of all conceptions of space. In the same manner all geometrical principles, e.g. ‘that in every triangle two sides together are greater than the third,’ are never to be derived from the general concepts of side and triangle, but from an intuition, and that a priori, with apodictic certainty.
5. Space is represented as an infinite quantity. Now a general concept of space, which is found in a foot as well as in an ell, could tell us nothing in respect to the quantity of the space. If there were not infinity in the progression of intuition, no concept of relations of space could ever contain a principle of infinity.
Of Time
I. Time is not an empirical concept deduced from any experience, for neither coexistence nor succession would enter into our perception, if the representation of time were not given a priori. Only when this representation a priori is given, can we imagine that certain things happen at the same time (simultaneously) or at different times (successively).
II. Time is a necessary representation on which all intuitions depend. We cannot take away time from phenomena in general, though we can well take away phenomena out of time. Time therefore is given a priori. In time alone is reality of phenomena possible. All phenomena may vanish, but time itself (as the general condition of their possibility) cannot be done away with.
III. On this a priori necessity depends also the possibility of apodictic principles of the relations of time, or of axioms of time in general. Time has one dimension only; different times are not simultaneous, but successive, while different spaces are never successive, but simultaneous. Such principles cannot be derived from experience, because experience could not impart to them absolute universality nor apodictic certainty. We should only be able to say that common experience teaches us that it is so, but not that it must be so. These principles are valid as rules under which alone experience is possible; they teach us before experience, not by means of experience.1
IV. Time is not a discursive, or what is called a general concept, but a pure form of sensuous intuition. Different times are parts only of one and the same time. Representation, which can be produced by a single object only, is called an intuition. The proposition that different times cannot exist at the same time cannot be deduced from any general concept. Such a proposition is synthetical, and cannot be deduced from concepts only. It is contained immediately in the intuition and representation of time.
V. To say that time is infinite means no more than that every definite quantity of time is possible only by limitations of one time which forms the foundation of all times. The original representation of time must therefore be given as unlimited. But when the parts themselves and every quantity of an object can be represented as determined by limitation only, the whole representation cannot be given by concepts (for in that case the partial representations come first), but it must be founded on immediate intuition.
Of Ideas in General
In spite of the great wealth of our languages, a thoughtful mind is often at a loss for an expression that should square exactly with its concept; and for want of which he cannot make himself altogether intelligible, either to others or to himself. To coin new words is to arrogate to oneself legislative power in matters of language, a proceeding which seldom succeeds, so that, before taking so desperate a step, it is always advisable to look about, in dead and learned languages, whether they do not contain such a concept and its adequate expression. Even if it should happen that the original meaning of the word had become somewhat uncertain, through carelessness on the part of its authors, it is better nevertheless to determine and fix the meaning which principally belonged to it (even if it should remain doubtful whether it was originally used exactly in that meaning), than to spoil our labour by becoming unintelligible.
Whenever therefore there exists one single word only for a certain concept, which, in its received meaning, exactly covers that concept, and when it is of great consequence to keep that concept distinct from other related concepts, we ought not to be lavish in using it nor employ it, for the sake of variety only, as a synonyme in the place of others, but carefully preserve its own peculiar meaning, as otherwise it may easily happen that the expression ceases to attract special attention, and loses itself in a crowd of other words of very different import, so that the thought, which that expression alone could have preserved, is lost with it.
From the way in which Plato uses the term idea, it is easy to see that he meant by it something which not only was never borrowed from the senses, but which even far transcends the concepts of the understanding, with which Aristotle occupied himself, there being nothing in experience corresponding to the ideas. With him the ideas are archetypes of things themselves, not only, like the categories, keys to possible experiences. According to his opinion they flowed out from the highest reason, which however exists no longer in its original state, but has to recall, with difficulty, the old but now very obscure ideas, which it does by means of reminiscence, commonly called philosophy. I shall not enter here on any literary discussions in order to determine the exact meaning which the sublime philosopher himself connected with that expression. I shall only remark, that it is by no means unusual, in ordinary conversations, as well as in written works, that by carefully comparing the thoughts uttered by an author on his own subject, we succeed in understanding him better than he understood himself, because he did not sufficiently define his concept, and thus not only spoke, but sometimes even thought, in opposition to his own intentions.
Plato knew very well that our faculty of knowledge was filled with a much higher craving than merely to spell out phenomena according to a synthetical unity, and thus to read and understand them as experience. He knew that our reason, if left to itself, tries to soar up to knowledge to which no object that experience may give can ever correspond; but which nevertheless is real, and by no means a mere cobweb of the brain.
Plato discovered his ideas principally in what is practical,1 that is, in what depends on freedom, which again belongs to a class of knowledge which is a peculiar product of reason. He who would derive the concept of virtue from experience, and would change what at best could only serve as an example or an imperfect illustration, into a type and a source of knowledge (as many have really done), would indeed transform virtue into an equivocal phantom, changing according to times and circumstances, and utterly useless to serve as a rule. Everybody can surely perceive that, when a person is held up to us as a model of virtue, we have always in our own mind the true original with which we compare this so-called model, and estimate it accordingly. The true original is the idea of virtue, in regard to which all possible objects of experience may serve as examples (proofs of the practicability, in a certain degree, of that which is required by the concept of reason), but never as archetypes. That no man can ever act up to the pure idea of virtue does not in the least prove the chimerical nature of that concept; for every judgment as to the moral worth or unworth of actions is possible by means of that idea only, which forms, therefore, the necessary foundation for every approach to moral perfection, however far the impediments inherent in human nature, the extent of which it is difficult to determine, may keep us removed from it.
The Platonic Republic has been supposed to be a striking example of purely imaginary perfection. It has become a byword, as something that could exist in the brain of an idle thinker only, and Brucker thinks it ridiculous that Plato could have said that no prince could ever govern well, unless he participated in the ideas. We should do better, however, to follow up this thought and endeavour (where that excellent philosopher leaves us without his guidance) to place it in a clearer light by our own efforts, rather than to throw it aside as useless, under the miserable and very dangerous pretext of its impracticability.

Immanuel Kant, Critique of Pure Reason [1881]
Of Space
By means of our external sense, a property of our mind, we represent to ourselves objects as external or outside ourselves, and all of these in space. It is within space that their form, size, and relative position are fixed or can be fixed. The internal sense by means of which the mind perceives itself or its internal state, does not give an intuition of the soul itself, as an object, but it is nevertheless a fixed form under which alone an intuition of its internal state is possible, so that whatever belongs to its internal determinations must be represented in relations of time. Time cannot be perceived externally, as little as space can be perceived as something within us.
What then are space and time? Are they real beings? Or, if not that, are they determinations or relations of things, but such as would belong to them even if they were not perceived? Or lastly, are they determinations and relations which are inherent in the form of intuition only, and therefore in the subjective nature of our mind, without which such predicates as space and time would never be ascribed to anything?
In order to understand this more clearly, let us first consider space.
1. Space is not an empirical concept which has been derived from external experience. For in order that certain sensations should be referred to something outside myself, i.e. to something in a different part of space from that where I am; again, in order that I may be able to represent them as side by side, that is, not only as different, but as in different places, the representation of space must already be there. Therefore the representation of space cannot be borrowed through experience from relations of external phenomena, but, on the contrary, this external experience becomes possible only by means of the representation of space.
2. Space is a necessary representation a priori, forming the very foundation of all external intuitions. It is impossible to imagine that there should be no space, though one might very well imagine that there should be space without objects to fill it. Space is therefore regarded as a condition of the possibility of phenomena, not as a determination produced by them; it is a representation a priori which necessarily precedes all external phenomena.
[3. On this necessity of an a priori representation of space rests the apodictic certainty of all geometrical principles, and the possibility of their construction a priori. For if the intuition of space were a concept gained a posteriori, borrowed from general external experience, the first principles of mathematical definition would be nothing but perceptions. They would be exposed to all the accidents of perception, and there being but one straight line between two points would not be a necessity, but only something taught in each case by experience. Whatever is derived from experience possesses a relative generality only, based on induction. We should therefore not be able to say more than that, so far as hitherto observed, no space has yet been found having more than three dimensions.]
4. Space is not a discursive or so-called general concept of the relations of things in general, but a pure intuition. For, first of all, we can imagine one space only and if we speak of many spaces, we mean parts only of one and the same space. Nor can these parts be considered as antecedent to the one and all-embracing space and, as it were, its component parts out of which an aggregate is formed, but they can be thought of as existing within it only. Space is essentially one; its multiplicity, and therefore the general concept of spaces in general, arises entirely from limitations. Hence it follows that, with respect to space, an intuition a priori, which is not empirical, must form the foundation of all conceptions of space. In the same manner all geometrical principles, e.g. ‘that in every triangle two sides together are greater than the third,’ are never to be derived from the general concepts of side and triangle, but from an intuition, and that a priori, with apodictic certainty.
5. Space is represented as an infinite quantity. Now a general concept of space, which is found in a foot as well as in an ell, could tell us nothing in respect to the quantity of the space. If there were not infinity in the progression of intuition, no concept of relations of space could ever contain a principle of infinity.
Of Time
I. Time is not an empirical concept deduced from any experience, for neither coexistence nor succession would enter into our perception, if the representation of time were not given a priori. Only when this representation a priori is given, can we imagine that certain things happen at the same time (simultaneously) or at different times (successively).
II. Time is a necessary representation on which all intuitions depend. We cannot take away time from phenomena in general, though we can well take away phenomena out of time. Time therefore is given a priori. In time alone is reality of phenomena possible. All phenomena may vanish, but time itself (as the general condition of their possibility) cannot be done away with.
III. On this a priori necessity depends also the possibility of apodictic principles of the relations of time, or of axioms of time in general. Time has one dimension only; different times are not simultaneous, but successive, while different spaces are never successive, but simultaneous. Such principles cannot be derived from experience, because experience could not impart to them absolute universality nor apodictic certainty. We should only be able to say that common experience teaches us that it is so, but not that it must be so. These principles are valid as rules under which alone experience is possible; they teach us before experience, not by means of experience.1
IV. Time is not a discursive, or what is called a general concept, but a pure form of sensuous intuition. Different times are parts only of one and the same time. Representation, which can be produced by a single object only, is called an intuition. The proposition that different times cannot exist at the same time cannot be deduced from any general concept. Such a proposition is synthetical, and cannot be deduced from concepts only. It is contained immediately in the intuition and representation of time.
V. To say that time is infinite means no more than that every definite quantity of time is possible only by limitations of one time which forms the foundation of all times. The original representation of time must therefore be given as unlimited. But when the parts themselves and every quantity of an object can be represented as determined by limitation only, the whole representation cannot be given by concepts (for in that case the partial representations come first), but it must be founded on immediate intuition.
Of Ideas in General
In spite of the great wealth of our languages, a thoughtful mind is often at a loss for an expression that should square exactly with its concept; and for want of which he cannot make himself altogether intelligible, either to others or to himself. To coin new words is to arrogate to oneself legislative power in matters of language, a proceeding which seldom succeeds, so that, before taking so desperate a step, it is always advisable to look about, in dead and learned languages, whether they do not contain such a concept and its adequate expression. Even if it should happen that the original meaning of the word had become somewhat uncertain, through carelessness on the part of its authors, it is better nevertheless to determine and fix the meaning which principally belonged to it (even if it should remain doubtful whether it was originally used exactly in that meaning), than to spoil our labour by becoming unintelligible.
Whenever therefore there exists one single word only for a certain concept, which, in its received meaning, exactly covers that concept, and when it is of great consequence to keep that concept distinct from other related concepts, we ought not to be lavish in using it nor employ it, for the sake of variety only, as a synonyme in the place of others, but carefully preserve its own peculiar meaning, as otherwise it may easily happen that the expression ceases to attract special attention, and loses itself in a crowd of other words of very different import, so that the thought, which that expression alone could have preserved, is lost with it.